Solved – How to use Turnbull’s nonparametric estimator for interval-censored data in R

If you want the Non-Parametric Maximum Likelihood Estimator (NPMLE) (what Turnbull 1976's algorithm computes), you could use the interval package.

I believe the default uses the standard EM algorithm as presented by Turnbull…but this is just about the slowest algorithm out there for computing the NPMLE. This could be a problem with n > 500, for example (also depends on the number of unique interval times). In interval, you can chose other faster algorithms with the initfit option; for example, I believe currently the fastest option would be to set initfit = 'initcomputeMLE'. The package also includes various plotting and testing functions.

Currently, the fastest algorithm available is ic_np in the icenReg package (note: this is the author). This can be fit as

npmle_fit <- ic_np(cbind(l, r) ~ 0, data = myData)

(where l and r are variables for the left and right side of the intervals in the dataset myData). And the plot can be produced by

plot(npmle_fit)

However, this is currently not compatible with the interval functions, which can do a lot more with the NPMLE than just plot it. So unless speed is really a huge issue, you may want to stick with interval.